The vehicle failed to stop while driving along Edinburgh Road in the city at 1.55pm on Saturday.
Officers followed the car before it crashed on the A90 near St Madoes, around six miles away.
The police vehicle was not involved in the crash.
According to Traffic Scotland, at around 2.20pm the road was closed between St Madoes and Kinfauns in both directions with southbound lanes open again by 4.30pm.
Four people who were in the car were taken to Ninewells Hospital in Dundee.
A Police Scotland spokeswoman said: "Around 1.55pm on Saturday, 20 February, a car failed to stop when signalled by police on Edinburgh Road in Perth.
"The vehicle was subsequently pursued. It was then involved in a crash on the A90 near St Madoes.
"The road is currently closed and enquiries are ongoing. Four occupants from the car have been taken to Ninewells Hospital in Dundee.”